Z-Scores

Name:

Class:

Date:

Show your work for each problem.

1.
Test scores have mean $\mu = 50$ and standard deviation $\sigma = 5$ . What is the z-score of a score of $60$ ?
1. a)-2
2. b)10
3. c)2
4. d)0.5
2.
A distribution has $\mu = 40$ and $\sigma = 4$ . Find the z-score of $x = 46$ .
3.
A value $x = 18$ comes from a distribution with $\mu = 12$ and $\sigma = 3$ . Find its z-score.
4.
A value has a z-score of $z = -1.5$ . What does that mean?
1. a)It is 1.5 standard deviations below the mean
2. b)It is 15% below the mean
3. c)It is 1.5 points below the mean
4. d)It is 1.5 standard deviations above the mean
5.
Adult weights in a group have $\mu = 65$ kg and $\sigma = 10$ kg. What is the z-score of a person who weighs $47$ kg?
6.
A distribution has $\mu = 60$ and $\sigma = 5$ . Which value has the z-score $z = -2$ ?
7.
Four students wrote different tests. Who did best compared with the others who wrote the same test?
1. a)Ben: 85 points (μ = 75, σ = 10)
2. b)Ana: 78 points (μ = 70, σ = 4)
3. c)Cleo: 90 points (μ = 84, σ = 6)
4. d)Dan: 66 points (μ = 60, σ = 5)
8.
Scores on a national test have $\mu = 500$ and $\sigma = 100$ . Which score has the z-score $z = -1.2$ ?
9.
Nora runs 5 km in $24$ min (her club: $\mu = 27$ min, $\sigma = 2$ min) and swims 100 m in $75$ s (her club: $\mu = 80$ s, $\sigma = 4$ s). Lower times are better. In which sport is she relatively better? Give the z-score of that sport.
10.
IQ scores have $\mu = 100$ and $\sigma = 15$ . Which score is unusual ( $|z| > 2$ )?
1. a)75
2. b)85
3. c)134
4. d)120
11.
In a school's 100 m race the times have $\mu = 13.5$ s and $\sigma = 0.6$ s. Find the z-score of a time of $12.6$ s.
12.
A phone battery lasts on average $\mu = 40$ hours with $\sigma = 3$ hours. One battery lasts only $33.4$ hours. Is that unusual?
13.
Resting heart rates of teenagers have $\mu = 72$ beats per minute and $\sigma = 8$ . Find the range of usual values, from $z = -2$ to $z = 2$ .
14.
A teacher adds 5 bonus points to every student's score. What happens to each student's z-score?
1. a)It decreases by 5
2. b)It increases by 5/σ
3. c)It increases by 5
4. d)It stays the same
15.
A test has mean $\mu = 80$ . A score of $92$ has the z-score $z = 1.5$ . What is the standard deviation $\sigma$ ?
16.
Scores on an entrance exam have $\mu = 1050$ and $\sigma = 200$ . A scholarship needs a z-score of at least $1.75$ . What is the lowest score that qualifies?
17.
In a class, a score of $78$ has the z-score $z = 1.5$ and the standard deviation is $\sigma = 6$ . What is the class mean $\mu$ ?
18.
On a test, a score of $70$ has $z = -1$ and a score of $94$ has $z = 2$ . Find the standard deviation $\sigma$ and the mean $\mu$ . Give $\mu$ as the final answer.